The Characterisation of Viscous Flow. Viscosity, Shear Rate and Shear Stress

Abstract

When considering flow characterisation in what are commonly regarded as liquids it becomes necessary to examine a number of variables. The overall characterisation is attained when all the relationships—including the interdependent cross-relationships—of an all-embracing rheological equation have been evaluated. The most general rheological equation is

$$\eta = F\left( {\gamma ,T,t,P,c,...} \right)$$

where η = coefficient of viscosity, ẏ = shear rate (itself a function of the shear stress), T = temperature, t = time, P = pressure (itself a function of volume), c = concentration, and where the multiple dots which follow include, for example, molecular parameters such as molecular weight (MW), molecular weight distribution (MWD), compositional variables such as crystallinity, the presence of additives (plasticisers, fillers, slip agents, mould release agents, pigments and dyes, stabilisers, products of decomposition and other impurities) and factors which relate to the processing history (orientation, residual stresses, etc.). Clearly such an equation is unrealistic and we shall therefore consider each of the principal variables in turn, assuming that the others remain constant.